Introductory Lectures on Automorphic Forms

Walter L. Baily

Published by Princeton University Press 1973

Introductory Lectures on Automorphic Forms

Walter L. Baily

Volume 1810 in the series Publications of the Mathematical Society of Japan

In the series Princeton Legacy Library

https://doi.org/10.1515/9781400867158

Overview
Contents

About this book

Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn).

Part I, essentially elementary, deals with complex analytic automorphic forms on a bounded domain; it presents H. Cartan's proof of the existence of the projective imbedding of the compact quotient of such a domain by a discrete group. Part II treats the construction and properties of automorphic forms with respect to an arithmetic group acting on a bounded symmetric domain; this part is highly technical, and based largely on relevant results in functional analysis due to Godement and Harish-Chandra. In Part III, Professor Baily extends the discussion to include some special topics, specifically, the arithmetic propertics of Eisenstein series and their connection with the arithmetic theory of quadratic forms.

Unlike classical works on the subject, this book deals with more than one variable, and it differs notably in its treatment of analysis on the group of automorphisms of the domain. It is concerned with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so is distinct from other modern treatises that deal with automorphic forms on a semi-simple Lie group.

Having had its inception as graduate- level lectures, the book assumes some knowledge of complex function theory and algebra, for the serious reader is expected to supply certain details for himself, especially in such related areas as functional analysis and algebraic groups.

Originally published in 1973.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Topics

Frontmatter Publicly Available Download PDF	i
Introduction Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	xi
Supplementary Notational References Requires Authentication Unlicensed Licensed Download PDF	xv
PART I. Elementary Theory of Automorphic Forms on a Bounded Domain
Chapter 1. General Notions and Examples Requires Authentication Unlicensed Licensed Download PDF	3
Chapter 2. Analytic Functions and Analytic Spaces Requires Authentication Unlicensed Licensed Download PDF	10
Chapter 3. Holomorphic Functions and Mappings on a Bounded Domain Requires Authentication Unlicensed Licensed Download PDF	26
Chapter 4. Analysis on Domains in Cⁿ Requires Authentication Unlicensed Licensed Download PDF	34
Chapter 5. Automorphic forms on bounded domains Requires Authentication Unlicensed Licensed Download PDF	43
Part II. Automorphic forms on a bounded symmetric domain and analysis on a semi-simple Lie group
Chapter 6. Examples for algebraic groups Requires Authentication Unlicensed Licensed Download PDF	53
Chapter 7. Algebraic groups Requires Authentication Unlicensed Licensed Download PDF	82
Chapter 8. Representations of compact groups Requires Authentication Unlicensed Licensed Download PDF	102
Chapter 9. Some work of Harish-Chandra Requires Authentication Unlicensed Licensed Download PDF	130
Chapter 10. Functional analysis for automorphic forms Requires Authentication Unlicensed Licensed Download PDF	169
Chapter 11. Construction of automorphic forms Requires Authentication Unlicensed Licensed Download PDF	186
Part III. Some special topics
Chapter 12. Fourier Coefficients of Eisenstein Series Requires Authentication Unlicensed Licensed Download PDF	225
Chapter 13. Theta Functions and Automorphic Forms Requires Authentication Unlicensed Licensed Download PDF	243
Bibliography Requires Authentication Unlicensed Licensed Download PDF	253
Index Requires Authentication Unlicensed Licensed Download PDF	259